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The easiest derivation of rod's moment of inertia?

by Glyper
Tags: derivation, easiest, inertia, moment
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Jan20-13, 09:52 AM
P: 27
1. The problem statement, all variables and given/known data
Derive the formula for rod's moment of inertia: I = ml2/12

2. Relevant equations
I = ml2/12

3. The attempt at a solution
The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some easier (or more "natural"?) way to do it? Or, if not, maybe you know some website where it's explained as if I were five so that I can get the grasp of it? Because looking at bare integrals, I don't quite know what I'm calculating.
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Jan20-13, 10:14 AM
HW Helper
P: 6,202
I think the easiest way would be to just do the integral.

I= ∫ r2 dm

If you consider a small infinitesimal piece at a distance 'dr' from the center of mass of the rod, the mass of this piece will be dm.

Then you just use the fact that mass = mass per unit length * distance i.e. dm = M/L * dr
Jan20-13, 11:06 AM
P: 27
I see. Thanks :)

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